sessions get killed while working on the system

Hello every1

I am new to System Administration I am facing an issue with my sessions (telnet ,SSH ,or FTP)they get killed most of the time while working on the system and sometimes if i keep them ideal they might stay all night without getting killed and once they get killed the connection gets lost and can not relogin to the server unless you wait for few seconds and that does not happen to all the sessions like if i open 4-5 sessions only 1 or 2 get killed and no specific time and cannot login to the server at that time but i can work normally on the alife sessions have any1 faced this before and I have opened tikets with HP support they said no issues found on the server and security and network guys response was we checked we could not find any issues yeah one more thing i never so connection breaks if telnet from diffrent server on the same network to the server